Relations as connection between two or more things are a familiar aspect of everyday life and conversation and are peculiar to mathematics. [1] In the treatment of relations by the English philosopher Francis Herbert Bradley (1846-1924) two important parts of the problem of relations become apparent: the nature of relations and the reality of relations. These two parts of the problem are closely related. It seems that the answer to the first part prescribes the answer to the second part. In this section we shall deal with these two parts of the problem of relations. Special reference will be made to F. H. Bradley's and Bertrand Russell's treatment of the problem.
Bradley's fundamental metaphysical distinction is appearance and reality. His chief work on metaphysics, Appearance and Reality, is divided into two parts according to this distinction. Part one is on appearance and part two is on reality. In part one Bradley relegates many traditional metaphysical concepts like substance, qualities, cause, to the realm of appearance. Among these so treated is the concept of relation. Thus Bradley answers the second part of the problem of relations - the part concerning their reality. Relations, according to Bradley, are appearance and not reality.
In order to establish his view concerning the reality of relations Bradley expounds on the nature of relations. Bradley argues that relations are nothing intelligible either with or without their terms. Relations without terms seem mere verbiage.
"For myself, a relation which somehow precipitates terms which were not there before or a relation which can get on somehow without terms and with no difference beyond the mere ends of a line of connection is really a phrase without meaning. It is, to my mind, a false abstraction and a thing which loudly contradicts itself." [2]Bradley argues that if relations without their terms or qualities are mere verbiage or unintelligible, then so are relations, on the other hand, with their terms or qualities, unintelligible. For how can relations stand to their terms or qualities? If a relation is nothing to the qualities, then they are not related at all; and, if qualities are not related at all, then they have ceased to be qualities and their relation is a nonentity. (Bradley holds that "relation presupposes quality, and quality relation," [3] which idea is very questionable.) But on the other hand, if a relation is to be something to them, then a new connecting relation is required.
"For the relation hardly can be the mere adjective of one or both of its terms and being something itself. If it does not itself bear a relation to the terms, in which intelligible way will it succeed in being anything to them?" [4]This leads to an endless regress of finding relations to relate the terms.
Bradley also argues against the reality of relations by saying that in a proper interpretation of them all relations are internal. He argues that when we make judgments, we predicate one thing of another. If in saying that x is y, and x and y are the same, then we are uttering a bare tautology, "x is x." If x and y are different, we are saying that x is what it is not, and this is unacceptable. Not only the relation of judgments, but all relations share the same inner difficulties. If x is related to y - any x, any y, and any relation - either the relation is something additional to x and y, or it is not. If it is not something additional, then the relation must be internal to x or y. But if the relation is internal on one side, so must it be on the other, and x and y become identical. If the relation is external, it has no anchor in x and y; and so the internal relation must relate x and y by two further relations; and at this point the same alternatives recur. The effect of holding that in "xRy" the relation "R" is internal to "x" and "y," is to make a single entity of "x" and "y." Ultimately, the result is a strongly monistic view of reality, which is Bradley's metaphysical purpose.
Thus Bradley argues for the unreality of relations, that is, that relations are appearances. In support of his claim of the unreality of relations he has appealed to the nature of relation. While most other philosophers are not so radical as to deny completely the reality of relations (it served Bradley's metaphysical purposes to deny the reality of relations and other metaphysical entities as well), they have gone as far as to deny the independent reality of relations and to assert that relations are reducible to some kind of substance or a quality. In any case, the denial of the reality or the independent reality of relations stems from some view about the nature of relations. Thus the problem of the nature of relations may be stated. Are relations only a particular kind of substance or a particular kind of attribute of quality or do they have an independent character of their own so that they are not reducible to either a particular kind of substance or quality?
The question of the nature of relations can be examined by breaking our
discussion up into three parts:
(a) Are relations a special kind of substance or thing?
(b) Are relations a special kind of attribute or quality?
(c) Or do relations have an independent, irreducible character of their
own?
The first question could be asked in several ways. They would all amount to the same thing and the absurdity of the idea of relations as a special kind of substance would still be immediately apparent. Bradley points this out in the argument we have recounted above. If relations are things, then this leads to an infinite regress of attempting to find relations to do the job of relating. None of the relations would actually relate. Each time a fresh relation is introduced it would fail and another new relation would have to be tried. It also may be argued that since a substance is that which by definition does not relate but is related, it is absurd to think of relations as some kind of a substance.
The idea that relations are a special kind of attribute or quality seems on the face of it more plausible than the previous idea that relations are a special kind of substance or thing. At least in the history of philosophical thought it has been considered plausible and even has been espoused by some philosophers. According to Mr. Johnson, for example, relations are qualities or a specific sort of qualities, and all propositions which employ terms that presupposes the reality of a third kind of entity may be reduced to propositions that assert qualities or a specific sort of qualities of a substantive. [5] Mr. Johnson goes on to argue that if one can show that there are specific sort of qualities, then one has by that very fact demonstrated that relations are definable in terms of qualities, and do not constitute a third kind of entity in addition to substantives and qualities.
J. N. E. McTaggart cites three arguments against the conclusion that relations can be reduced to qualities.
The second of these arguments deserves further attention. For in it we have curious turn: the reality of certain qualities is made to depend upon the presence of a relation. A relation generates a property in each of the terms that it relates. If A admires B, then A has the property of admiring B and B has the property of being admired by A. These kinds of properties are usually known as relational properties. They are derived from a relation. And if the relation does not exist, then the properties cease also. A no longer has the property of admiring B and B is no longer being admired by A. It would seem rather absurd to say that relations are definable in terms of qualities and do not constitute a kind of entity different from substantives or qualities. The converse seems to be nearer the truth.
It would seem that if relations are neither substantives nor a special kind of quality, then they must have an independent and irreducible character of their own. They may belong to another group of entities but what that group is, is not at all clear and for the time being such hypothetical groups shall be left out of our discussion.
A word must be said about Bertrand Russell's arguments for the independent and
irreducible character of relations. Russell's arguments seem to be based on
the confusion about the relation of the following two propositions:
(1) that there are no exemplifications of relations in the actual world,
that is, those relations are unreal, and
(2) that every proposition may be stated in the subject-predicate form.
Most philosophers with the exception of the metaphysical skeptics and
positivists would agree that proposition (1) implies proposition (2). For we
believe that the propositions we assert are somehow relevant to the actual
world and reality, that is, they are rendered either true or false by
reference to it. And if there are no relations, then any fact about the
actual world must be expressible in a proposition with a subject-predicate
form and any proposition not in that form must be reducible to that form.
While it is true that proposition (1) implies proposition (2), it is not true
that proposition (2) implies proposition (1). Proposition (2) merely asserts
that for every proposition not in a subject-predicate form we can construct a
logically equivalent proposition in the subject-predicate form. It does not
assert that there are no entities called relations corresponding to the words
indicating relations. Bertrand Russell seems to think that proposition (2)
does imply proposition (1). And it is for this reason that this argument for
independent reality of relations seems to turn around the denial that every
proposition may be expressed in the subject-predicate form and the assertion
that relational propositions are not logically equivalent formally to one or
more subject-predicate propositions.
Paul Marhenke in his lecture on the reality of relations published in the volume titled Studies in the Problem of Relations has observed that
"Common-sense as exemplified in its linguistic usage presupposes the reality of relations. It is illegitimate, however, to turn to common-sense for a final answer to the question: Are relations real? Logicians have often condemned language as an unreliable guide in the analysis of logical questions. Nevertheless, if it were not for the fact that the propositions we think are crystallized in language, our logical analyses would have been abortive from the start. This is an obvious truism. We may have to refer to other considerations than those of language in order to get a satisfactory answer to such questions. At any rate language gives us a least a provisional answer to the question: Are relations real? And that answer is in the affirmative." [7]But in spite of the fact that ordinary language seems to presuppose the reality of relations, some philosophers have denied their reality. Let us briefly inquire into the reasons why they have been declared unreal. As we have already indicated the denial of their reality stems chiefly from a particular view about their nature. Relations may be exhibited as a kind of quality and thus be denied any independent reality. This is the position that W. E. Johnson adopts. If one can show that relations are a specific sort of quality one has by that very fact demonstrated that relations do not constitute a third kind of entity in addition to substantives or qualities. McTaggart points out another way the reality of relations may be denied.
"The chief reason which has been given for the rejection of relations is that there is nowhere for them to be. They are not, it is clear, in either of the terms without being in the other. Nor are they in each of them, taken separately. They are, it is said, between the terms, and not in them. Then, it is asked, is there anything in which they can be? And when this is answered in the negative, it is concluded that they are impossible." [8]This line of argument supposes that a relation must be something like a quality and must therefore have something in which it is or inheres. Otherwise, relations are impossible. As McTaggart notes:
"It takes, as the test of possibility of relations, the question whether they can behave exactly as qualities behave, and when it is admitted that they cannot, it concludes that relations are impossible, and that, in a true view of reality, judgments of relation would be replaced by judgments of quality." [9]McTaggart concludes that
"There is no justification for the assumption that a relation is impossible, if it cannot inhere in something as a quality does. To the question 'in what is a relation?' we may fairly answer that it is not in anything, but that it is between two or more terms, or between a term and itself, and that the conception of 'between' is as ultimate as the conception of 'in' and has as much claim to be regarded as valid." [10]Another reason for denying the reality of relations is a consequence of the application of Occam's razor. If one can develop a systematic logic or metaphysics with less, do not use more. This reason does not deny reality to relations, but on the other hand it does not affirm the reality of relations either. Those who deny reality to relations use Occam's razor to support their denial. According to Occam's razor, so they argue, even if there are relations, we are not obliged to make mention of them. For we can always express the fact that such and such terms stand in such and such relation by means of propositions which assert only qualities of those terms. While it is doubtful whether this can be done (Compare Paul Marhenke's treatment of W. E. Johnson's attempt. [11]) one can dispense with the mention of relations in one's logic if he so desires. What one does in one's logical system, however, has no bearing on the reality of relations. It seems to me, however, that one's logical system would be inadequate if he should fail to recognize the independent reality of relations.
[2] Bradley, F. H., Appearance and Reality, 32
(London, 1893).
[5] Johnson, W. E., Logic, I, Chapter I, Sec. 6; Chapter XIII
(Cambridge: Cambridge University Press, 1924).
[6] McTaggart, J. M. E., The Nature of Existence, I: 83.
[7] Marhenke, Paul, "The Reality of Relations," p. 167;
University of California Publications in Philosophy, Vol. 13,
Studies in the Problem of Relations,
George P. Adams, J. Loewenberg, Stephen C. Pepper (eds.)
(Berkeley, Calif.: University of California Press, 1930).
[11] Marhenke, Op. Cit., 187f.
Adams, George P., Loewenberg, J., Pepper, Stephen C. (eds.):
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Studies in the Problem of Relations
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